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TMF, 1999, Volume 119, Number 2, Pages 179–248 (Mi tmf736)  

This article is cited in 13 scientific papers (total in 13 papers)

On the Riemann–Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schrödinger equation: Interacting fermion case

A. R. Itsa, N. A. Slavnovb

a IUPUI, Department of Mathematical Sciences
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the local field dynamic temperature correlation function of the quantum nonlinear Schrödinger equation with a finite coupling constant. This correlation function admits a Fredholm determinant representation. The related operator-valued Riemann–Hilbert problem is used to analyze the leading term of the large time and distance asymptotic expansion of the correlation function.

DOI: https://doi.org/10.4213/tmf736

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English version:
Theoretical and Mathematical Physics, 1999, 119:2, 541–593

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Received: 28.10.1998

Citation: A. R. Its, N. A. Slavnov, “On the Riemann–Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schrödinger equation: Interacting fermion case”, TMF, 119:2 (1999), 179–248; Theoret. and Math. Phys., 119:2 (1999), 541–593

Citation in format AMSBIB
\by A.~R.~Its, N.~A.~Slavnov
\paper On the Riemann--Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schr\"odinger equation: Interacting fermion case
\jour TMF
\yr 1999
\vol 119
\issue 2
\pages 179--248
\jour Theoret. and Math. Phys.
\yr 1999
\vol 119
\issue 2
\pages 541--593

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    This publication is cited in the following articles:
    1. N. A. Slavnov, “Integral equations for correlation functions of a quantum one-dimensional Bose gas”, Theoret. and Math. Phys., 121:1 (1999), 1358–1376  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. R. K. Bullough, N. M. Bogolyubov, V. S. Kapitonov, K. L. Malyshev, I. Timonen, A. V. Rybin, G. G. Varzugin, M. Lindberg, “Quantum Integrable and Nonintegrable Nonlinear Schrödinger Models for Realizable Bose–Einstein Condensation in $d+1$ Dimensions $(d=1,2,3)$”, Theoret. and Math. Phys., 134:1 (2003), 47–61  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Caux, JS, “One-particle dynamical correlations in the one-dimensional Bose gas”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P01008  crossref  mathscinet  isi  scopus  scopus  scopus
    4. Kozlowski K.K., Terras V., “Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrodinger model”, J Stat Mech Theory Exp, 2011, P09013  crossref  isi  scopus  scopus  scopus
    5. Kozlowski K.K., Maillet J.M., Slavnov N.A., “Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas”, J Stat Mech Theory Exp, 2011, P03018  crossref  isi  scopus  scopus  scopus
    6. Kitanine N. Kozlowski K.K. Maillet J.M. Slavnov N.A. Terras V., “Form Factor Approach to Dynamical Correlation Functions in Critical Models”, J. Stat. Mech.-Theory Exp., 2012, P09001  crossref  mathscinet  isi  elib  scopus  scopus  scopus
    7. Patu O.I. Kluemper A., “Correlation Lengths of the Repulsive One-Dimensional Bose Gas”, Phys. Rev. A, 88:3 (2013), 033623  crossref  adsnasa  isi  elib  scopus  scopus  scopus
    8. Its A.R., Kozlowski K.K., “On Determinants of Integrable Operators With Shifts”, Int. Math. Res. Notices, 2014, no. 24, 6826–6838  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Its A.R., Kozlowski K.K., “Large- x Analysis of an Operator-Valued Riemann?Hilbert Problem”, Int. Math. Res. Notices, 2016, no. 6, 1776–1806  crossref  mathscinet  zmath  isi  elib  scopus
    10. Brun Ya., Dubail J., “One-Particle Density Matrix of Trapped One-Dimensional Impenetrable Bosons From Conformal Invariance”, SciPost Phys., 2:2 (2017), UNSP 012  crossref  isi
    11. Kozlowski K.K., “On the Thermodynamic Limit of Form Factor Expansions of Dynamical Correlation Functions in the Massless Regime of the Xxz Spin 1/2 Chain”, J. Math. Phys., 59:9, SI (2018), 091408  crossref  mathscinet  zmath  isi  scopus
    12. Zhi-Qiang Li, Shou-Fu Tian, Wei-Qi Peng, Jin-Jie Yang, “Inverse scattering transform and soliton classification of higher-order nonlinear Schrödinger–Maxwell–Bloch equations”, Theoret. and Math. Phys., 203:3 (2020), 709–725  mathnet  crossref  crossref  isi  elib
    13. Gharakhloo R., Its A.R., Kozlowski K.K., “Riemann-Hilbert Approach to a Generalized Sine Kernel”, Lett. Math. Phys., 110:2 (2020), 297–325  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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